On the precision models of fringe projection profilometry: unification, simplification and connection

Shenzhen Lv; Nengqi Huang; Yuxuan Zou; Chengeng Liu; Siah Yee Long; Dawei Tang; Xiangqian Jiang; Qian Kemao

doi:10.1038/s41377-026-02300-x

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On the precision models of fringe projection profilometry: unification, simplification and connection

Original Articles

- On the precision models of fringe projection profilometry: unification, simplification and connection
- Light: Science & Applications Vol. 15, Issue 8, Pages: 2611-2628(2026)
- Affiliations：
  
  1.College of Computing and Data Science, Nanyang Technological University, Singapore, Singapore
  2.Centre for Precision Technologies, University of Huddersfield, Huddersfield, UK
- Author bio：
  
  Qian Kemao (mkmqian@ntu.edu.sg)
- Funds：
- DOI：10.1038/s41377-026-02300-x
  CLC：
- Received：28 November 2025，
  
  Revised：2026-03-29，
  
  Accepted：04 April 2026，
  
  Online First：12 May 2026，
  
  Published：31 August 2026
- Accepted：
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Lv, S. Z. et al. On the precision models of fringe projection profilometry: unification, simplification and connection. Light: Science & Applications, 15, 2611-2628 (2026).
DOI：

Lv, S. Z. et al. On the precision models of fringe projection profilometry: unification, simplification and connection. Light: Science & Applications, 15, 2611-2628 (2026). DOI： 10.1038/s41377-026-02300-x.

摘要

Abstract

Fringe projection profilometry (FPP) is one of the most prominent non-interferometric high-precision 3D shape measurement techniques for measuring dimensions ranging from 1 mm to 1 m

with increasing applications in precision engineering. Thorough theoretical understanding of the precision of the prevailing FPP methods is critical when facing the challenges of higher precision demands. In this paper

through theoretical analysis of three reconstruction methods based on the projection of vertical fringes (Ver3)

horizontal fringes (Hor3) and optimal-angle fringes (OptE3)

we establish a general unified precision model

from which a general Pythagoras relationship is discovered

clarifying the optimal precision of OptE3. We then simplify the model to reveal the role of a system’s geometry for easier configuration. First

a special yet not restrictive case where the direction of the optical axis of the projector is perpendicular to the baseline of the FPP is considered

resulting in an intermediate unified precision model. We show that the effective baselines of the three methods obey a special Pythagoras relationship. Second

the angle between the optical axes of the camera and the projector is interestingly delineated from the projector’s extrinsic parameters

leading to our final and simplified unified precision model. This simplified model is geometrically tangible and thus eases the determination of the positions and orientations of the projector and camera in system configuration

given a precision budget

for which

an FPP-Planner software tool is prototyped. Going beyond

we theoretically equivalate FPP with stereo vision and laser triangulation regarding precision. Our findings are experimentally validated. These theoretical models are believed to potentially enhance or even change the way of FPP design and performance evaluation.

关键词

Keywords

references

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